Printscreen the active Window only?

ALT + Printscreen should do the trick!

then simply paste your image in paint or the image editing application of your choice and save it, no cropping required.

Alt + Printscreen does the job, but then you have to paste into some app - and save.

Use Cropper in stead, which will not interfer with the normal PrintScreen-behaviour - but add a feature that saves the captured image directly to a folder of your choise in jpg for instance. Works great when you want to do many screenshots.

Irfanview allows you do this.

Go to Options->Capture/Screenshot (or press 'C'), and then select the Capture Area you want (e.g. foreground window), then start.

Select the window you want to capture, then press Ctrl-F11. Irfanview will then come to the front, with your captured window as an image, ready for you to save and/or edit as needed.

For Vista and Windows 7 I can recommend WindowClippings as that program is able to produce PNGs with transparency where the glass frame is. Thus you don't have parts of other windows shining through, you get the round corners cleanly cut out and you get the DWM drop shadow for free. Definitely useful, although not as much for people using legacy Windows versions.

It comes at a small price, however.